The present invention relates generally to double resonating beam force transducers and double ended tuning fork (DETF) sensors, and in particular to double resonating beam force transducers and DETF sensors decoupled from a support structure and a method of determining a decoupled resonator beam structure.
Typical double resonating beam force transducers and double ended tuning fork (DETF) sensors have two tines having constant widths. The tines terminate in solid base regions at each end of the beam, where the beam is tied into the support structure of the transducer. The tine terminations may be of various shapes, as described in U.S. Pat. No. 4,724,351 to Eernisse et al, which is incorporated in its entirety herein by reference. The Eernisse et al patent also describes tines of non-constant width.
A problem arises when the resonator beam is vibrated: the longitudinal motion of the ends of the tines is coupled through base regions to the support structure of the transducer. This coupling acts to reduce the Q factor of the resonator beam, and changes the resonator beam""s frequency. The continual transfer of energy from the resonator to the surrounding structure due to longitudinal motion of the base regions is commonly referred to as an xe2x80x9cend pumpingxe2x80x9d effect.
Other double resonating beam force transducers and double ended tuning fork (DETF) sensors have two constant-width tines with additional lateral teeth to aid in driving the resonator beam through electrical attraction to similar toothed structures. The additional lateral driver teeth on the tines tends to increase the end pumping effect of the coupling.
An additional problem arises in devices having multiple resonators, which is common in accelerometers and similar devices. The coupling of one resonator into the support structure can transmit energy to the other resonators in the device and change their frequency. These changes in frequency lead to errors in indicated force.
Prior art solutions, such as those disclosed in the Eernisse et al patent, for reducing the effects of coupling have been to stiffen the midsection of the tines, shape the tine cross section, or modify the root of the tine near the base region where the beam is connected to the support structure. However, forming such irregular tine shapes presents manufacturing challenges.
The present invention provides a resonator beam that overcomes the limitations of the prior art by providing a resonator beam structure that, during vibration of the tines, minimizes coupling of a longitudinal motion of the tines into a support structure to which the resonator beam is attached. The resonator beam includes a pair of tines having a first and a second end; a first base region mechanically coupling together the first ends of the tines; a second base region mechanically coupling together the second ends of the tines; a first cutout at a first predetermined position in a closed interior portion of the first base region and having a first predetermined geometry; and a second cutout at a second predetermined position in a closed interior portion of the second base region and having a second predetermined geometry.
The first and second predetermined positions are positions that are predetermined to minimize, during vibration of the tines, coupling of the longitudinal motion of the tines into a support structure to which the resonator beam is attached. The predetermined position of the first cutout is a position that is adjacent to the first end of the tines; and the predetermined position of the second cutout is a position that is adjacent to the second end of the tines.
The first and second predetermined geometries are geometries that are predetermined to minimize, during vibration of the tines, coupling of the longitudinal motion of the tines into a support structure to which the resonator beam is attached. The predetermined geometries are, for example, rectangular shapes having respective first and second predetermined sizes. The first and second predetermined geometries are, for example, substantially identical.
The invention also provides a method using finite element analysis techniques for determining optimal geometries and positions for cutouts in the enlarged or widened base regions of the resonator beam structure that, during vibration of the tines, minimizes coupling of a longitudinal motion of the tines into a support structure to which the resonator beam is attached.